Convergence of Euro Area Inflation Rates

Transcription

1 MPRA Munch Personal RePEc Archve Convergence of Euro Area Inflaton Rates Claude Lopez and Davd Papell Banque de France, Unversy of Houston 2010 Onlne at MPRA Paper No , posted 7. March :24 UTC

2 Convergence of Euro Area Inflaton Rates Claude Lopez * Banque de France Davd H. Papell ** Unversy of Houston March 3, 2011 Abstract We study the behavor of nflaton rates among the 12 nal Euro countres n order to test whether and when the group convergence nally dctated by the Maastrcht treaty and now by the ECB, occurs. We also assess the mpact of events such as the advent of the Euro and the 2008 fnancal crss. Due to the small sze of the estmaton sample, we propose a new procedure that ncreases the power of panel un root tests when used to study group-wse convergence. Applyng ths new procedure to Euro area nflaton, we fnd strong and lastng evdence of convergence among the nflaton rates soon after the mplementaton of the Maastrcht treaty and a dramatc decrease n the persstence of the dfferental after the occurrence of the sngle currency. After the 2008 crss, Euro area nflaton rates follow the ECB s prce stably benchmark, although Greece reports relatvely hgher nflaton. JEL: C32, E31 Keywords: groupwse convergence, nflaton, Euro area, 2008 crss * Internatonal Macroeconomcs Dvson, Banque de France, 31 rue crox des pets champs, Pars cedex 01, France, Tel : Emal: Claude.Lopez@banque-france.fr ** Department of Economcs, Unversy of Houston, Houston, TX Tel: +1 (713) Emal: dpapell@uh.edu We thank Phlppe Bacchetta, Paul Evans, Chrs Murray, and partcpants at the Mdwest Econometrc Group, Purdue Unversy, Sam Houston State Unversy, Southern Economc Assocaton, Socety for Nonlnear Dynamcs and Econometrcs and Banque de France meetngs for helpful comments and dscussons. Lopez would lke to acknowledge the fnancal support of the Taft Research Center.

3 1. Introducton Inflaton rates and ther convergence whn the Euro area have been a major concern snce well before the advent of the sngle currency. The recent fnancal crss and s strong mpact on several Euro area countres wh hgher nflaton rates have strengthened ths nterest, especally n the lght of the European Central Bank s (ECB) objectve of prce stably. Snce 1999, the ECB has clearly stated that Euro Area nflaton should be mantaned below but close to 2% n the medum run. Assessng whether Euro area nflaton rates satsfy such a convergence snce the advent of the sngle currency s que challengng due to the lmed amount of avalable data and the poor performance of standard tme seres technques typcally used to test whether convergence has occurred. We address ths ssue n two steps. Frst, we nvestgate groupwse convergence among Euro area nflaton rates usng an mproved testng procedure and focusng on the 12 nal members whch share a common Euro perod. Then, we look at whether these nflaton rates respect the ECB s benchmark, both as a group and ndvdually. Tme seres nvestgaton of the convergence hypothess often reles on un root tests. The rejecton of the null hypothess s commonly nterpreted as evdence that the seres have converged to ther equlbrum state, snce any shock that causes devatons from equlbrum eventually des out. The extenson of these tests to the panel framework has sgnfcantly nfluenced the lerature on how to measure convergence of macroeconomc varables. Panel un root tests for convergence among seres, or group-wse convergence, utlze Bernard and Durlauf s (1995, 1996) defnon of tme seres convergence for long-run output movements, where two (or more) countres have converged when long-run forecasts of per capa output dfferences tend to zero as the forecastng horzon tends to nfny. In the bvarate context, tests for tme seres convergence requre cross-country per capa output dfferences to be statonary. 1 In the multvarate or panel context, a group of countres have converged f the null hypothess that the dfference between each country s output and the cross-sectonal mean has a un root can be rejected n favor of the alternatve hypothess that each dfference s statonary. 2 Several works use panel methods to nvestgate output convergence (Ben-Davd (1993, 1996), Islam (1995), Evans and Karras (1996), Evans (1998), 1 Clearly, the tme seres defnon of convergence mples that the seres have reached the state of equlbrum and not that they are adjustng toward. 2 Pesaran( 2007) suggests an alternatve to test for parwse convergence of ouput. 1

4 and Flessg and Strauss (2001), among others) or nflaton convergence ( Lee and Wu (2001), Kočenda and Papell (1997) and Weber and Beck (2005), among others). Whle panel un root tests have sgnfcantly enhanced fne sample performance when compared to the unvarate approach, these tests can stll have low power to reject the un root null n a panel of statonary seres f the panels consst of hghly persstent seres, contan a small number of seres, and/or have seres wh a lmed length. Ths paper proposes a new procedure that mproves the fne sample power of panel un root tests when testng for group-wse convergence and uses the procedure to analyze the behavor of the nflaton rates across the Euro area, solatng pror and Euro perods. The suggested method uses nformaton known pror to estmaton. Panel un root tests for group-wse convergence nvolve statonary between a group of seres and ther cross-sectonal means. As the seres may not be characterzed by absolute convergence toward the cross-sectonal average, each dfferental can have a non-zero mean. By constructon, however, the group of dfferentals has a cross-sectonal average of zero for each tme perod. In order to mprove the panel un root test s performance, we explo ths extra nformaton on the data by ncorporatng the approprate restrcton when estmatng the model and generatng fne sample crcal values. Monte Carlo smulatons confrm the enhanced fne sample performance of the test when usng the constrant. To our knowledge, ths constrant has not been utlzed for prevous tests of convergence usng panel un root tests. 3 The mproved performance n small samples allows us to focus on a smaller data span whle mantanng the relably of the analyss. In partcular, enables us to solate the estmaton perod from 1999:1 to 2006:12, startng wh the advent of the Euro and endng before the 2008 fnancal crss. The study analyzes Euro area nflaton rates from 1979:1 to 2010:04 by constructng a rollng wndow of eght years, startng wh 1979:1-1986:12 and endng wh 2002:5-2010:4. The wndows startng n 1999:1 account for the Euro perod whle the wndows startng n 2001:1 nclude the 2008 fnancal crss. Ths rollng wndow approach also deals wh any potental tme break n the data due to events such as German reunfcaton. 3 It should be emphaszed that our proposed method s only applcable for tests of group-wse convergence. The power of panel un root tests that examne the Purchasng Power Pary hypothess by nvestgatng the statonary of real exchange rates, for example, cannot be mproved by our method as, n ths case, the seres are ndvdually convergng to ther own mean but not to a common target. 2

5 The frst part of our analyss shows that nflaton rates whn the Euro area share a common pattern: they have converged or report a stable relaton among themselves as early as just after the mplementaton of the Maastrcht treaty and ths convergence remans strong untl after the advent of the Euro. The results also hghlght the temporary mpact of the 2008 fnancal crss: an nal weakenng of the un root rejectons s shortly followed by strengthened evdence of convergence for most of the groups observed. The rate of persstence of the dfferentals, whch s drectly lnked to the degree of convergence among the nflaton rates, hghlghts four phases: () perods endng between 1986:12 and 1997:8, where the Maastrcht crera are not fully mplemented and the persstence s que hgh but stable; () perods endng between 1997:9 and 2004:12, whch s a perod of transon from mplementng the Maastrcht treaty to the advent of the Euro, where the persstence vares a lot, wh an nal drastc decrease that s later partally compensated; () perods endng between 2005:12 and 2007:12, the Euro perod, where the persstence s, once agan, stable, yet at a lower level than n the nal perod and, fnally, perods endng after 2008:09 that nclude the 2008 fnancal crss. 4 The descrbed behavor follows closely the European Monetary Unon tme table. The generated medan unbased estmates, ther 95% confdence ntervals and the correspondng half-lves confrm a dramatc decrease n the persstence of the dfferentals after the occurrence of the sngle currency. The second part of the analyss focuses on the ECB s objectve and on ndvdual devatons from. The results confrm that the unque currency sgnfcantly anchors the ndvdual and cross-sectonal volatly of the Euro area nflaton rates, especally for less wealthy countres such as Greece, Portugal, and Span. 5 Euro area nflaton s very close to 2% for most of the Euro perod wh the excepton of the 2008 fnancal crss. However, at the country level, Ireland, Greece, and Span relax ther efforts shortly after the adopton of the sngle currency, endng up wh notceably hgher nflaton rates than the other Euro countres, placng them n a strong dsadvantage n term of prce competveness and susceptble to current account defcs and bubbles (real estate: Span, Ireland, publc debt: Greece). Whle these three countres are the most affected among the group by the crss, ths 4 Whle the euro started n 1999, fxed pares among the currences were set n The same queston cannot be nvestgated for Ireland as s monthly data starts only n

6 event seems to act as a realgnment for ther nflaton wh the rest of the group for Span and Ireland, but not for Greece. 2. Panel Un Root Tests for Convergence 2.1 Group-wse stochastc convergence In the panel framework, testng for (stochastc) convergence of a group of N tme seres requres studyng the dynamc propertes of the seres dfferental wh respect to the cross sectonal mean. Group-wse (stochastc) convergence mples that: (1) Where I t represents the nformaton set avalable at tme t. If =0, the convergence follows Bernard and Durlauf (1996) s defnon of absolute convergence. If 0 the convergence s sad to be condonal or relatve as defned by Durlauf and Quah (1999), whch mples that the seres have converged toward a tme-nvarant equlbrum dfferental Panel un root test We modfy standard panel un root tests to account for the restrcton on the ntercepts when testng for group-wse convergence. More specfcally, we focus on the second generaton of panel un root tests that account for contemporaneous correlaton by estmatng the resdual covarance matrx. The test consdered s an extenson of the Levn, Ln, and Chu (2002) applcaton of the ADF test to the panel framework that nvestgates a homogeneous rate of convergence across the seres. Let consder the followng system of ADF regressons: y wh c y, t1 k j1 y, t j 1,..., N t 1,..., T and j ~ WN(0; ) (2) where = s the homogeneous rate of convergence, k j the lagged frst dfferences that account for seral correlaton and the non-dagonal covarance matrx. The null and alternatve hypotheses tested are 0 and 0. 6 The dfferentals wll be statonary f eher the seres and the cross-sectonal mean are both I(0) or f they are both I(1) and contegrated. 4

7 The pooled ADF test reles on feasble generalzed least squares (SUR) method, hence the name ADF-SUR test. It s performed n two steps. Frst, for each seres, k j s selected wh the recursve lag-selecton procedure of Hall (1994). Then, the resduals covarance matrx s deduced and used to estmate (2) wh the SUR method, constranng the values of to be dentcal across equatons and usng k j. Fnally, the estmated and s correspondng standard devaton allow us to calculate the t- statstcs correspondng to the null = 0. Snce the focus of the paper s on a panel of macroeconomc varables where the tme seres dmenson s large compared to the cross-secton dmenson, s assumed that T > N. Whle would be desrable to allow for heterogeneous rates of convergence, the choces are problematc. 7 Followng Im, Pesaran, and Shn (2003), several tests that average t- statstcs across the members of the panel have been developed. 8 The alternatve hypothess for these tests, however, s that 0 for at least one, whch s not economcally relevant for nvestgatng convergence among a group of countres. The tests developed by Breuer, McNowan, and Wallace (2002), whch allow to be heterogeneous across countres n a framework smlar to (2), provdes (at best) modest ncreases n power over unvarate tests. 2.3 The new testng procedure Our testng procedure benefs from extra knowledge avalable about the data and desgns a model that accounts for all nformaton avalable pror to the estmaton. More specfcally, ths non-sample nformaton s ncluded as a restrcton n the estmaton and when generatng the fne sample crcal values. The restrcton beng true by constructon, the fnal estmator ends up wh a smaller varance than the unrestrcted one. Greene (2008, p89) suggests that one way to nterpret ths reducton n varance s as the value of the nformaton contaned n the restrcton. 9 The procedure reles on the knowledge that, once transformed, the data may have a non-zero mean for each dfferental but a cross-sectonal mean equal to 0 at every perod. If dff y s the dfferental for country at tme t wh respect to the cross-sectonal mean such 7 Breung and Pesaran (2005) survey the exstng lerature and pont out that, n both the homogenous and the heterogeneous cases, the rejecton of the null hypothess means that "a sgnfcant fracton of the cross-secton uns s statonary". 8 An alternatve s to use a factor structure approach as n Ba and Ng (2004). 9 Judge et al. (1988, p812) explans that f nonsample nformaton s correct, then usng n conjuncton wh the sample nformaton wll lead to an unbased estmator that has a precson matrx superor to the unrestrcted least squares estmator. 5

8 dff that y y y / N 1 dfferentals s equal to 0, that s N ; then by constructon, for each perod of tme t, the sum of the N 1 y dff N 1 y N 1 N y =0. Let replace y by dff y n (2), then the ntercepts c are on average equal to 0. Hence, the estmaton uses the restrcton N 1 c 0. Note that, snce each regresson allows for an ntercept, we are not testng for absolute convergence. The resultng system of equatons s: y dff wh c y dff 1 dff where s the homogenous rate convergence, and k j1 y dff j 1,..., N t 1,..., T and j y ~ WN (3) s the data dfferental wh respect to the cross-sectonal mean. The error terms ( 1t,..., ) are statonary wh a non-dagonal Nt covarance matrx. The standard hypotheses, H 0 : = 0 versus H 1 : < 0, are tested. The estmaton procedure follows three steps: 1. Data transformaton: the dfferentals wh respect to the cross-sectonal mean are calculated for all seres 2. Lag selecton: the number of lagged frst dfference terms allowng for seral correlaton, k n (3), s selected usng the recursve procedure for each seres 3. Estmaton: The resdual covarance matrx s estmated. The resultng ˆ, along wh the pre-selected k, s then used n the estmaton of (3) wh the SUR method whle two restrctons are mposed: N a. c 0, that s the non-sample nformaton 1 b. =, that s a homogeneous rate of convergence The estmated and s correspondng standard devaton are obtaned, and the t-statstc s calculated for H 0 : = 0. The nterpretaton of the two restrctons s very dfferent. (a) s true by constructon, and therefore there s no queston whether or not s correct. (b) s almost surely false, as 6

9 there s no reason why each country should have the same rate of convergence. There are two ways, however, for the restrcton of homogeneous convergence rates to be false. Frst, all of the 0. In that case, rejecton of the un root null correctly provdes evdence of convergence. Second, some of the 0 and some of the 0. In that case, there s a mxed panel and rejecton of the un root null does not correctly provde evdence of convergence. We consder the performance of our test wh mxed panels below. O Connell (1998), Maddala and Wu (1999), and Lopez (2009a), among others, show that panel un root tests estmatng the resdual covarance matrx should rely on smulated crcal values to reduce any sze dstortons due to the cross-sectonal correlaton, whle Chang (2004) proves the asymptotc valdy of a seve bootstrap procedure for non-pvotal homogeneous panel un root tests. As a result, the bootstrap crcal values are generated usng the followng non-parametrc resamplng method wh replacement: frst, the bootstrap nnovatons from y dff * u are obtaned by resamplng wh replacement the emprcal resduals estmated the resduals k j1 y j dff, t j u. 10 The contemporaneous correlaton s preserved by resamplng * u as a vector. Next, the bootstrap samples * t are recursvely generated usng * * * * the estmated parameters ( ˆ j ) and the bootstrap samples u t as ˆ j, t u, startng from,..., dff * u 0 u, k 1. Fnally, the pseudo-data y are obtaned by takng the partal sum of * k dff* dff* * as y y j. 11 The estmaton procedure explaned n Secton 2.3 s then 0 j1 appled and the t-statstc calculated. Ths procedure s erated 1000 tmes, the resultng vector of t-statstcs s then sorted to calculate eher the data specfc crcal values or the p- values. Each estmaton requres s own set of crcal values to be generated. Davdson and G. MacKnnon (2006) explan that mposng the restrcton [ ] yelds more effcent estmates of the nusance parameters upon whch the dstrbuton of the test statstcs may depend. Ths generally makes bootstrap test more relable, because the k j1 10 The emprcal resduals were, frst, centered then resampled. 11 * Each pseudo-data y dff s generated wh T+50 observatons, then the frst 50 observatons are dscarded, dff * hence each y s random. 0 7

10 parameters of the bootstrap DGP are estmated more precsely. Snce the restrcton s true by constructon, we expect the restrcted test to perform better n small samples than the unrestrcted one. 2.4 Impact of the constrant n small samples In order to analyze the mpact of the restrcton c 0, a set of smulatons nvestgates the fne sample performance of the ADF-SUR test wh and whout the restrcton. Let consder the followng data generatng processes: y y, t1 u, t N 1 wh =1,,N and t=1,,t The nnovatons u are drawn from d normal dstrbutons wh mean zero and a dagonal covarance matrx. 12 The panel dmensons are N = 5, 10, and 20 and T = 25, 50, 100, and 200. For each experment, the fne sample crcal values and the emprcal rejecton probables calculated at a 5% nomnal level are based on 2000 eratons. 13,14 Snce we are usng randomly generated data, each experment s repeated 20 tmes, hence Tables 1 and 2 report the average rejecton probables. Table 1 reports the fne sample propertes of both restrcted and unrestrcted ADF- SUR tests. The data sets are generated under the null hypothess ( = 1.00) for the sze and under the alternatve ( = 0.99, 0.97, 0.95 and 0.90) for the sze adjusted power. 15 Both tests report almost no sze dstorton wh a probably of rejectng the un root null when the data have one, close the nomnal sze of 5%. However, the tests sgnfcantly dffer n ther ably of rejectng accurately the null hypothess when analyzng statonary data. For example, for hghly persstent data such that (N, T, ) = (10, 100, 0.97), the restrcton ncreases the szeadjusted power of the ADF-SUR test from to Smlarly, for moderately persstent data such that (N, T, ) = (20, 50, 0.95), the restrcton ncreases the power from to As expected, these mprovements dsappear as N and T ncrease and the data s less persstent, that s n the cases where the ADF-SUR test performs well. In addon, the 12 Smlar smulatons have been reproduced usng non-dagonal matrx covarance, that s ncludng and accountng for contemporaneous correlaton, whout any sgnfcant change regardng the mpact of the restrcton on the ntercept. 13 Davdson and McKnnon (1999) advse a mnmum of 1500 bootstraps when analyzng the performance of the test at 1%. 14 Davdson and McKnnon (2006) defne and dscuss ths probably for the power and sze of bootstrap tests 15 The case = 0.8 s not reported as does not provde any new nsghts on the test s behavor. 8

11 restrcton has only a moderate mpact when the panel has a small tme dmenson, T = 25 and 50, and the data s extremely persstent, = In sum, the restrcton sgnfcantly enhances the test s performance for persstent data ( > 0.9) and small to medum data spans (T < 200). Table 2 focuses on the test s performance when the data s not generated under the alternatve hypothess of homogeneous and statonary rates of convergence but as a mx of statonary and non-statonary processes. More specfcally, some seres converge at a same rate ( == 0.97, 0.95, 0.90 and 0.8 for = 1,,k) whle others follow a non-statonary process ( j = 1.0 for j = k+1,, N). 16 The data length T s equal to 100 for N = 5, 10 and 20. Such an experment allows us to nvestgate whether the mproved fne sample performance of the restrcted test leads to an ncrease n unwanted rejectons of the null hypothess over the unrestrcted test. Indeed, Taylor and Sarno (1998) and Breuer, McNowan, and Wallace (2001) have provded evdence that, n the general case where the sum of the ntercepts s not constraned to equal zero, the un root null can be rejected by panel methods wh homogeneous rates of convergence even when the panels contan only a few statonary seres. Breuer, McNowan, and Wallace (2002), Sarno and Taylor (2002), and Taylor and Taylor (2004) go further, argung that the un root null can be rejected even f only one of the seres s statonary. To address ths concern, we frst look at the bottom row of Table 2, for N = 5, 10, and 20, that reports the (correctly szed 0.05) rejecton frequences when all seres have a un root. Gong up one row, the rejecton frequences for both the restrcted and the unrestrcted tests are depcted when one of the seres s statonary, that s (, j ) = (, 1.00) for = 1 and j = 2,,N. For N = 5, they range from 0.07 ( = 0.97) to 0.11 ( = 0.8), for N = 10, they range from 0.06 ( = 0.97) to 0.08 ( = 0.8) and, for N = 20, they range from 0.06 (= 0.97) to 0.07 ( = 0.8). Hence, seems very unlkely that the ncluson of one statonary seres wll produce a rejecton of the un root null wh any of these tests. 17 Whle the argument that ncluson of one statonary seres wll produce rejectons usng panel un root tests wh homogeneous rates of convergence seems overstated, the results confrm that one needs to be careful about nterpretng rejectons of the null as 16 The case = 0.99 s not reported as does not provde any new nsghts on the test s behavor. 17 Some of our rejecton frequences whout the constrant are lower than n Breuer, McNowan, and Wallace (2001) for dentcal panels. The dfferences appear to be due to ther use of Levn, Ln, and Chu (2002) crcal values whch do not account for seral correlaton. Papell (1997) dscusses ths ssue. 9

12 evdence that all of the seres are statonary. For example, wh N = 10, both tests report a rejecton frequency of about 0.50 wh 8 statonary seres f = Snce the result of rejecton or non-rejecton would be analogous to the outcome of a con flp, one would not want to conclude n favor or aganst the null hypothess. Yet, s worth notng that, for all three panels wh a mx of un root and less persstent ( = 0.9 and 0.8) statonary seres, the rejecton frequences for the restrcted test are smaller than those for the unrestrcted test. Hence, one would be less lkely to falsely reject the un root null hypothess for most of the cases when usng the restrcted ADF-SUR test. For the panels wh a mx of un root and more persstent ( = 0.95 and 0.97) statonary seres, the rejecton frequences for the restrcted tests are stll smaller or equal to those for the unrestrcted tests except n presence of very few (up to three dependng the panel) un roots. In practce, however, one s much less lkely to falsely reject the un root null wh restrcted than wh unrestrcted ADF-SUR tests. Ths s because, wh hghly persstent processes and N = 5 or N = 10, the tests do not have much ably to reject the un root null even when all of the seres are statonary. Takng the most extreme example (N, ) = (5, 0.97) for emphass, the 5% sze adjusted power s only 0.41 for the restrcted test and 0.23 for the unrestrcted test when all of the seres are statonary. Wh one statonary seres, the fact that the rejecton frequency s larger for the restrcted (0.22) than the unrestrcted (0.16) test s unlkely to cause an napproprate concluson as the restrcted test under rejects the null hypothess around 80% of the tme. A very dfferent pcture emerges wh less persstent processes where the tests are often able to approprately reject the un root null when all of the seres are statonary. We wll focus on a comparson of the rejecton frequences between the two tests for the smallest number of statonary seres for whch the rejecton frequency of the unrestrcted test s 0.50 or hgher. For N = 5, the rejecton frequency s 0.58 for the restrcted test and 0.65 for the unrestrcted test wh 4 statonary seres and = 0.9 and s 0.40 for the restrcted test and 0.51 for the unrestrcted test wh 3 statonary seres and = 0.8. Wh N = 10, the rejecton frequency s 0.57 for the restrcted test and 0.66 for the unrestrcted test wh 7 statonary seres and = 0.9 and s 0.54 for the restrcted test and 0.64 for the unrestrcted test wh 6 statonary seres and = 0.8. When N = 20, the rejecton frequency s 0.46 for the restrcted test and 0.56 for the unrestrcted test wh 11 statonary seres and = 0.9 and s 0.42 for the 10

13 restrcted test and 0.53 for the unrestrcted test wh 9 statonary seres and = 0.8. In the above examples, both tests very often reject the un root null when all of the seres are statonary, so they represent cases where s plausble that the un root null mght be rejected wh a mxture of statonary and non-statonary seres. Whle other examples could be chosen, the pattern s clear. For mxed panels that contan less persstent statonary seres wh = 0.8 or = 0.9, one s less lkely to mstakenly reject the un root null hypothess wh the restrcted than wh the unrestrcted tests. When the data s, by constructon, restrcted so that the sum of the ntercepts s equal to zero for each perod, the gan n effcency obtaned by mposng the restrcton n the estmaton has two man mpacts on the ADF-SUR test. 18 Frst, the more precse estmaton and resultng bootstrap procedure leads to a more powerful sze-adjusted test for the most commonly encountered panel dmensons n macroeconomcs. Second, the rejecton frequences are generally smaller for mxed panels of statonary and non-statonary processes. Combnng the results, the restrcton mproves the overall behavor of the test, enhancng s ably to correctly reject the un root null hypothess when all seres are statonary and to correctly fal to reject the un root null when a subset of the seres are non-statonary. 3. Inflaton convergence whn the Euro Area In lght of the achevement of the Maastrcht crera, the fxng of Euro area exchange rates n md-1998, and the establshment of the Euro n January 1999, one would expect Euro area nflaton rates to have converged durng the perod mmedately precedng the advent of the sngle currency. Ths expectaton s confrmed by numerous studes, ncludng Rogers, Hufbauer and Wada (2001), Engel and Rogers (2004), Weber and Beck (2005), Busett, Forn, Harvey and Vendt (2007) and Rogers (2007), whch agree that prces were less dspersed and nflaton rates among Euro area countres have converged n the md-1990s. In contrast, research nvestgatng the post-1998 perod, ncludng ECB (2003), Honohan and Lane (2003), Engel and Rogers (2004), Weber and Beck, (2005), Rogers (2007), and Frsche and Kuzn (2008), concludes that the advent of the Euro resulted n the weakenng of nflaton convergence among the Euro area countres and n an ncrease n ther prce dsperson. An 18 The gan n effcency refers to the more precse estmaton that leads to smaller varance of the error terms. 11

14 excepton s Honohan and Lane (2004), who report sharp convergence n nflaton rates snce The ECB s prce-stably polcy mples that as a whole the Euro area should have a yearly nflaton equal to or less than 2%. If such a goal s acheved then Euro area nflaton rates should have (group-wse) converged toward a cross-sectonal mean of 2% or less. Our study contrbutes towards understandng the behavor of the 12 nal Euro area nflatons and ther evoluton through tme by () nvestgatng the group behavor of the nflaton dfferentals wh respect to ther cross-sectonal mean and () lookng at ndvdual devatons from the group central tendency and from the ECB s benchmark. We frst nvestgate the evoluton of group-wse convergence over tme, startng wh the perod pror to the European Monetary System and endng wh the post 2008 fnancal crss perod. Next, we hghlght the mpact of the Euro by comparng the estmated speeds of convergence before and after the adopton of the sngle currency as well as the post 2008 fnancal crss. Fnally, we focus on the ECB s 2% benchmark and how each nflaton rate compares to. 3.1 Behavor of Euro area nflaton rates as a group: groupwse convergence Annual nflaton rates wh monthly data for the th country at tme t are calculated such that: ln( CPI t ) ln( CPI t12). 19 The dfferentals y are generated so that: dff where t t s the cross-sectonal average nflaton rate. 20 Monthly CPI data are from Internatonal Fnancal Statstcs from 1979:1 to 2010:4. Euro 10 (E10) countres are Austra, Belgum, Fnland, France, Germany, Italy, Luxembourg, Netherlands, Portugal and Span, Euro 11 (E11) countres nclude Greece whle Euro 12 (E12) countres also nclude Ireland. 21 Fgure 1 reports the nflaton rates as well as the cross-country means, medans and standard devatons of the nflaton rates. The descrptve statstcs show an overall decrease for both the E10 and E11 panels. More specfcally, ths decrease occurs n three phases: has the steepest slope, followed by wh a flatter slope, and then early 2008 reports no vsble change n the slope. 22 Fnally, the last perod, from md-2008 to 19 The data s seasonally adjusted 20 Yearly nflaton wh monthly data and annualzed monthly average nflatons yeld to smlar results. 21 The monthly data for Ireland s avalable only startng 1998:1; hence the analyss based on E12 starts at that pont. 22 Lopez (2009b) shows that the Euro-zone nflaton rates are regme-wse statonary. 12

15 the end of the sample, presents some dvergences between the behavor of the mean, the medan and the standard devaton. For each group, the mean and the medan show a notceable ncrease, wh the hghest pont at md-2008; then a sgnfcant drop, wh the lowest level n md-2009 and concludes wh a level lower than pror to the crss. In contrast, the standard devaton for E10 and E11 remans que stable snce 2000, whle E12 shows an ncrease n nflaton dsperson snce md Note that the mean and the medan for E10 and E11 are very close snce 1997 and 2000, respectvely. Only E12 reports a mean lower than the medan for the year Ths ncrease n dsperson s coherent wh the notceable decrease n nflaton of Ireland reported n Fgure 4b. Fnally, the E10, E11 and E12 s cross sectonal means are very close or below to the 2% benchmark for the perods , and after The enhanced performance of the new estmaton procedure enables us to consder relatvely short perods whle preservng good sze adjusted power of the test. We choose an estmaton wndow of eght years as corresponds to the Euro and pror-fnancal crss perod of 1999:1-2006:12 (96 monthly observatons). The wndow s then rolled from 1979:1-1986:12 to 2002:5-2010:4, one month at a tme, provdng a detaled vew of the adjustments that took place throughout the EMS changes. Ths approach also lms the mpact of potental changes n the parameters on the estmaton results whle depctng the evoluton of the results through tme. In contrast to studes whch use a recursve (expandng) estmaton wndow to study convergence, our results are not affected by the fact that the power of panel un root tests ncreases wh the number of observatons as well as the sze of the panel. Fgure 2 reports p-values for all panels usng restrcted and unrestrcted ADF-SUR tests. 23 The three groups of countres lead to smlar conclusons. A comparson between the restrcted and the unrestrcted estmatons emphaszes the mpact of the prevously dscussed gan n precson wh the new estmaton procedure: whle the results observe a smlar pattern, the restrcted approach consstently leads to lower p-values. The fndngs based on restrcted estmaton show sporadc rejectons of the un root hypothess for pre-euro wndows endng n and These (lack of) results are mportant for two reasons. Frst, they emphasze how perod specfc the rejecton of the un root can be and the 23 For each wndow of estmaton, a new p-value s generated usng the bootstrap procedure explaned n Secton

16 necessy of reportng lastng evdence of convergence when concludng n favor of stably. Second, these scarce rejectons of the un root are coherent wh the troubles that EMS had durng the 1980s. The wndows endng n report the strongest evdence that convergence has occurred. Focusng on the restrcted estmaton, the un root null s rejected (at least at the 10 percent level) wh E10 for most of the wndows endng n 2000:9-2010:4. 24 Addng Greece (E11) leads to relatvely smlar results, wh rejecton at least at 10 percent of the un root for all the wndows endng n 2002:3-2009:2 and after 2009:10. In contrast, the addon of Ireland (E12) has a notceable mpact as the un root s almost never rejected after the wndow endng n 2009:2. The mpact of mposng the restrctons s very clear for the Euro perod, leadng to lastng evdence of convergence for E10 and E11, whle E12 reports a deteroraton of that evdence snce the 2008 fnancal crss. In the absence of the restrcton, evdence of convergence s sporadc after 2004 for E11 and almost dsappears for E10 and E12. It should perhaps be emphaszed that, for the partcular case of testng for group-wse convergence, there s no queston that mposng the restrcton that the sum of the ntercepts n Equaton (3) s equal to zero s the correct procedure. Unlke the usual case of mposng restrctons, whch may or may not be correct, ths restrcton s correct by constructon. Fgure 3 plots the values of for the restrcted model for E10, E11 and E12 from 1979:1-1986:12 to 2002:5-2010:4. In accord wh our defnon of (stochastc) convergence, varatons of can be nterpreted as a measure of the strength of nflaton group-wse convergence. As a result, a more persstent dfferental (hgher value of ) would correspond to an weaker convergence among Euro area nflaton rates as any shock would have a longer lastng mpact, and vce versa. 25 Unlke the p-values, the rate of convergence observes three clear perods. Frst, remans relatvely stable up to the wndow endng n 1997:3 (close to 0.96 for both panels, E10 and E11). Then, both panels report drastc changes: the wndows endng between 2002:2 and 2003:12, frst, report a sgnfcant reducton n persstence ( decreases from to for E10 and from to for E11), whch s then partally compensated by a strengthenng of the persstence ( ncreases from to There are no rejectons for the wndows endng n 2001:9-2002:1, 2005:7-2005:11, and 2009:1-2009:5. 25 In other words, the tme seres defnon of convergence s that the dfference between the seres s statonary. Hence, the rate of convergencemeasures the strength of the relatonshp among these seres. 14

17 for E10 and from to for E11) for the wndows endng n 2004:1-2004:12. Followng ths perod of transon, a perod of stably concludes the sample: the wndows endng between 2005:1 and 2010:04 report an average value for of for E10 and for E11. In contrast, E12 observes relatvely stable perod up to the wndow endng n 2009:1, then the average ncreases from to for the remanng of the sample. Both E10 and E11 end wh the strongest degree of convergence among the nflaton rates of the entre perod studed. The lower values of for the wndows startng n 2002:2 are consstent wh Honohan and Lane s (2004) evdence of convergence n Euro area nflaton rates snce In contrast, the E12 panel reports very dfferent results showng a weaker degree of convergence among ths group of nflaton rates (hgher than for E10 or E11), weakened even more after the fnancal crss. The behavor of both the p-values and the rates of convergence for E10 and E11 closely follow the European Monetary Unon (EMU) tmetable up to the fnancal crss. The mechansm that led to the sngle currency ncluded three major steps: from 1990:7 to 1993:12 (wndows endng n 1997:7-2000:12), capal was allowed to move freely whn the European Economc Communy, from 1994:4 to 1998:12 (wndows endng n 2001:4-2005:12) the Treaty of Maastrcht was mplemented and n 1999:1 (wndow endng n 2006:12), the sngle currency was ntroduced. Fnally, the 2008 fnancal crss s notceable, especally for E12, confrmng the mpact of the Irsh crss on the group convergence. Fnally, evdence of group-wse statonary for E10 and E11 occurs several years before the processes reach a steady level of persstence. Whle nflaton rates have converged shortly after the mplementaton of the Maastrcht treaty, they do not attan a stable level of convergence untl a year pror to the fxed pary between the exchange rates. Even though the 2008 fnancal crss led to a temporary ncrease n, whch reaches s hghest pont of wh the wndow endng n 2009:4 for E10 and of for E11, the fnal degree of convergence s sgnfcantly hgher ( s sgnfcantly lower) than the one estmated for the frst two phases of the EMU ( = and for E10 and E11, respectvely). 3.2 Behavor of Euro area nflaton rates as a group: measurng persstence 26 Whle the value of s based downward, the focus n the secton s on a comparson across tme perods whch would not be affected by bas correcton. In the next secton, we conduct medan-unbased estmaton for several wndows. 15

18 A closer nvestgaton of the mpact of the Euro and of the fnancal crss requres a more accurate measure of. Hence, we apply medan unbased correctons to the restrcted and the unrestrcted estmates. We focus on four wndows: 1982:7-1990:6, or the pre- Maastrcht era, 1990:7-1998:6, or the pre-euro perod, whch ends sx months before the exchange rates were defnely fxed, and two Euro perods: 1999:1-2006:12, just after the advent of the Euro and 2002:5-2010:4, whch ncludes for the 2008 fnancal crss. Followng Murray and Papell (2005), we use an extenson of the Andrew and Chen (1994) method to the panel framework. The orgnaly of our approach, however, conssts of generatng medan unbased estmates of the homogeneous rate of convergence for the restrcted model. The eratve procedure used to generate the approxmately medan unbased estmate, AMU, of n (3) starts wh the estmaton of n (3) va the new procedure. Then, j assumng the estmates of s are true, the frst medan unbased estmate j 1,AMU s obtaned by fndng the medan-unbased estmator that corresponds to the value of SUR-restrcted. We then assume 1,AMU to be the true value of and obtan a new set of estmates for the s. j Condonal on these news estmates, we obtan the new medan unbased estmates 2,AMU. The eratve process contnues untl convergence occurs and medan unbased estmates of SUR-restrcted and the j s are obtaned. Table 3 reports the rates of convergence for the dfferentals, the medan unbased estmates (pont estmates and 95% confdence ntervals of ), and the correspondng halflves. The medan unbased pont estmates are (as expected) hgher than the GLS estmates. The Euro perods are characterzed by the fastest rates of convergence, followed by the pre- Maastrcht perod, wh the pre-euro perod dsplayng the slowest convergence rates. Ths pattern holds for the E10 and E11 panels and the restrcted and unrestrcted estmates. 27 For example, usng the restrcted model, E10 demonstrates a strengthenng n group-wse nflaton convergence as decreases from for the pre-maastrcht perod and for the pre- MU Euro to for the Euro perods. As expected, there s no dfference between the restrcted and unrestrcted GLS estmates, because the restrcton s respected by the data. However, the restrcton leads to a 27 The only excepton s for the unrestrcted E10 panel, for whch the value of s slghtly lower for the pre-euro than for the pre-maastrcht perod. 16

19 smaller varance of the estmates whch s confrmed by the lower restrcted medan-unbased estmates across all perods. Smlarly, all the confdence ntervals when the restrcton s mposed are narrower than the unrestrcted confdence ntervals, confrmng the gan n precson from the restrctons dscussed above. 28 The 95% confdence ntervals for the Euro perods confrm the stronger evdence of convergence among the Euro area nflatons from the pont estmates. The confdence ntervals for the E10 panel wh the restrcted model wden between the pre-maastrcht (0.950 to 0.988) and the pre-euro (0.946 to 0.996) perods. In contrast, the confdence ntervals for the Euro perod (0.905 to and to 0.972) have a smaller upper bound and a much smaller lower bound than the confdence ntervals for the two earler perods. The persstence of an economc tme seres s commonly measured wh the half-lfe, the number of perods takes for a shock on the nflaton dfferental to dsspate by 50 percent. The half-lfe s approxmated by the rato ( ln( 0.5)/ln( ) ). 29 The medan unbased estmates and correspondng confdence ntervals for the half-lves provde a more explc llustraton of the speed of convergence. A larger half-lfe would mply slower decay and weaker nflaton group-wse convergence. Our results once agan llustrate the gan n nformaton when usng the restrcton: the restrcted HL MU pont estmates are consstently lower that unrestrcted estmates. More mportantly, the gan n precson leads to narrower restrcted confdence ntervals, wh a notceable dfference for the upper boundares. For the half-lves, every restrcted confdence nterval s narrower than the correspondng unrestrcted confdence nterval. Snce the restrctons are vald by constructon, we wll focus on the medan-unbased estmates of the restrcted model. The half-lves of the pont estmates for both E10 and E11 decrease by more than 40 percent between the pre-maastrcht and Euro perods and by more that 50 percent between the pre-euro and Euro perods: E10 (E11) s half-lves rose from (23.55) months n the pre-maastrcht perod to (98.67) months n the pre-euro MU 28 Whle the E11 panel for the pre-maastrcht perod appears to be an excepton, wh the wdth of the confdence nterval equal to 0.68 for the restrcted and 0.53 for the unrestrcted estmates, that nterpretaton s not correct. The upper pont of the confdence nterval for the unrestrcted model s Snce the confdence ntervals are constraned not to exceed uny, no comparson can be made n ths case. 29 Whle s generally preferable to compute half-lves from mpulse response functons, the panel model used allows for dfferent seral correlaton across seres, hence there s no common mpulse response functon on whch the half lfe could be based. 17

20 perod, followed by a declne to (10.31) months n the frst Euro perod and to (13.80) months after the 2008 crss. The half-lves for the E10 and E11 panels are very smlar for the pre-maastrcht and the frst Euro perod. They are, however, very dfferent for the pre-euro perod wh a drastc slowdown of the speed of convergence for E11 (ncrease n MU ) after the Maastrcht treaty, hghlghtng the mpact of Greece and s dffcultes n keepng s nflaton under control. Smlarly, E11 reports an ncrease n persstence n the last perod, when compared to the prevous perod and to E10, whch s coherent wh Greece s recent crss. The E12 panel exsts only for the Euro perods; yet, s estmates confrm an overall more persstent behavor than E10 and E11. An overall decrease n persstence and narrowng of HL MU s confdence ntervals for the Euro perods s a robust result through both E10 and E11 panels. Gong from the pre- Maastrcht to the pre-euro perod, the confdence ntervals of the half-lves wden for the E10 panel, due to the numerous changes Europe had n the early 1990s (German reunfcaton, dfferent economc polces) and s evoluton toward the more rgorous structure defned by the Maastrcht treaty. Smlarly, for the same perods, the confdence ntervals for the E11 panel ncrease and wden, agan reflectng the nfluence of the ncluson of Greece. However, as prevously reported for the pont estmates, the HL MU s confdence nterval of E11 has a hgher upper bound when the fnancal crss s ncluded. The persstence measured remans sgnfcantly lower than pror to the Euro, whch s n lne wh the message of Fgure 1: the nflatons report very smlar behavor except for Greece and Ireland. 3.3The ECB s goal of prce stably Can we reconcle our results wh the ECB s medum run target of a 2% nflaton rate or lower for the Euro area? We address ths queston by frst lookng at Euro area nflaton rates and then by solatng the countres wh consstently hgher rates. The average Euro area nflaton rates for E10, E11 and E12, reported n Fgure 4a, are close to the ECB s defnon of prce stably snce the advent of the Euro, wh few temporary out-of-target perods: , and end of It s worth notng that the perod of prce stably corresponds to the perods of group-wse convergence and of lower levels of persstence (.e strong convergence among the nflaton rates). Our results, also, show that the ncluson of Greece and Ireland weakened ths groupwse convergence, especally after the 2008 fnancal crss. A closer look at each ndvdual 18

21 country s nflaton rate provdes some nsghts on the type of convergence exstng whn the 12 nal Euro countres. Clearly, the nflaton rates can observe eher a smlar level of nflaton or consstently dfferent rates ( = 0 or 0 n Equaton 1, respectvely), whle stll respectng the ECB s goal of prce stably. We set as a benchmark the group of the seven lowest nflaton rates, E7, (Austra, Belgum, Fnland, France, Germany, Luxembourg, and Netherland). Fgure 4b plots the confdence ntervals correspondng to the E7 cross-sectonal mean plus/mnus two tmes s standard devaton and the nflaton rates of the fve remanng countres. 30 As a basc rule of thumb, any nflaton out of ths area s que dfferent from the seven others. Untl 2000, Greece, Ireland, Italy, Portugal, and Span report the hghest nflaton rates. Between 2000 and 2008, Greece and Span report nflaton rates that are among the hghest of the group whle Ireland s rate s clearly much hgher than the rest of the group. Such nflaton dfferentals mply a loss n relatve prce competveness for the countres wh hgher than average nflaton rates, leadng to ssues such as trade mbalances whn the sngle currency area. Hence, s not surprsng that Greece, Ireland and Span were the most affected by the 2008 crss whn the Euro area. After the crss, Ireland s nflaton rate falls precpously, causng real deprecaton that may help toward a faster recovery, unlke Span s nflaton that observes a moderate decrease. Concurrently, Greece stll reports a much hgher nflaton rate than the Euro area as a whole. Ireland and Greece offset each other mpact on the cross-sectonal mean of the group. As a result, the nflaton of the Euro area (based on the nal 12 countres) remans whn the ECB s benchmark. 4. Conclusons Ths paper nvestgates the behavor of nflaton rates whn the Euro area from 1979:1 to 2010:4. More specfcally, focuses on the mpact of events such as the advent of the Euro and the recent fnancal crss on the countres ably to follow ECB s prce stably creron. The analyss reles on rollng an 8-year wndow through the entre sample, from 30 Results qualatvely smlar have been obtaned by plottng the c when consderng dfferental wh respect to the E7 cross-sectonal mean for the same 5 countres. 19

22 1979:1-1986:12 to 2002:5-2010:4, solatng Euro perods that both do and do not nclude the 2008 crss. The man dffculty n focusng on such a short wndow of estmaton s the poor performance of standard tme seres tools. We propose a new estmaton procedure that can be used when nvestgatng convergence of a group of seres toward a common target. Groupwse tme seres convergence s commonly measured usng panel un root tests on dfferentals generated as the dfference between each seres and the cross-sectonal average. Hence, each resultng dfferental has a non-zero mean, but the cross-sectonal mean of the group of dfferentals s equal to zero for each perod. Our method uses that nformaton n order to ncrease the sze adjusted power of the test. Monte Carlo smulatons report notceable mprovements of the test s power, especally when the data s persstent data ( > 0.9) or when the data has a lmed length (T < 200). Both of these characterstcs are commonly featured n macroeconomc tme seres. Furthermore, the restrcted ADF-SUR test also shows a greater ably of rejectng the un root null solely when all the seres are statonary, whch s a welcome mprovement on one of the most acknowledged drawbacks of the panel un root approach. The ncrease n sze adjusted power from the mposon of the true restrcton allows us to estmate the model for the pre-maastrcht, pre-euro, and Euro perods. Our results show that, whle sporadc evdence of nflaton convergence begns shortly after the mplementaton of the Maastrcht treaty; steady evdence that the seres have converged only occurs durng the Euro perods. The medan-unbased estmate of the rate of convergence s much faster and the correspondng confdence ntervals are consderably narrower for the Euro perods than for the two earler perods. The half-lves of the pont estmates of the dfferentals, the number of perods that takes for a shock to the nflaton dfferentals to decrease by one-half, falls by more than 40 percent between the pre-maastrcht and Euro perods and by more that 50 percent between the pre-euro and Euro perods. The compellng evdence of group-wse convergence among the nal Euro area countres presented here for the Euro perods also leads to another mportant pont: ths same group of countres meets the ECB s objectve on prce stably. Ths result holds even when we show that a mnory of countres, namely Greece, Ireland and Span, report consstently hgher nflaton rates for most of the Euro perod. The resultng loss n prce competveness 20